Connected graph reduction
Task number: 4266
Prove that every connected graph on \( n \ge 3 \) vertices contains two vertices \( u \) and \( v \) such that all three graphs \( G \setminus \{u \} \), \( G \setminus \{v \} \) and \( G \setminus \{u, v \} \) are connected.
Hint
Try the farthest vertices possible.
